I hand-coded my website from the ground up with a text/code editor, so I wouldn’t say no one is doing it.
As Steve said, WordPress is the most popular CMS for general small- and medium-sized sites. Personally, it’s not my favorite CMS, but it’s relatively simple compared to Joomla or Drupal, and there are tons of online resources and add-ons available from thousands of developers. If the site is more specialized, such as this forum or an e-commerce site, more specialized CMSs are often a better bet than WordPress.
I’d stay away from the drag-and-drop website builders, such as Wix or Weebly, however. They don’t measure up for professional-quality business purposes.
I wouldn’t hand-code it from the ground up, but there’s a good chance I’d hand-code or modify an existing template or theme using a code editor. That would likely only be for five-figure and up sites, though.
For smaller sites with modest needs and budgets, an off-the-shelf framework/theme would work if it came with some good backend customization features — Elegant Theme’s Divi, for example.
There really is no standard way of building websites, however. Every team goes about it differently with their own preferred set of tools and workflows.
My workplace offered websites in Wordpress unless it was specifically an e-commerce site. I can’t speak to if our devs pulled a theme and then edited the e-commerce site or what… but for our simple websites, we always used Wordpress.
We did switch between using the builders Elementor, Beaver Builder, and Divi.
Personally, I love Divi with Wordpress and if I pursue freelance web work I plan on using it.
There isn’t an industry standand website building platform.
I think the best platform depends on your needs, your team, the budget and your technical capabilities.
Some designers produce their designs in Illustrator, then pass them off to team of developers to translate them into code.
Other designers build the website themselves using drag and drop site builders like WIX, while some tech-savy designers will just code the whole thing themselves from scratch or tweak an existing template on a CMS to do what they want.
If you don’t want to play with coding, you can build simple, but visually unconstrained sites, (ie template-free, starting with a blank page and designing as you would a blank page for print – though, obviously, the parameters are different), then have a look at Sparkle (terrible name, but don’t let that put you off). It is not expensive. It is, however, Mac only.
There are templates, if you so choose. You can add in your own code in a limited way, without having to go under the bonnet (hood) and incorporate things like e-commerce.
There is no built in CMS, which is a minor problem. (Then again, any larger, feature-rich sites, I’d use something like XD, Figma or Sketch them and hand them over to a developer, anyway.) If you are using Sketch already, you can pull layouts straight into Sparkle. You can password protect pages (as of newest version, released a couple of days ago).
In short, you can produce great sites without touching code, if you want. Best successor to Adobe’s Muse, I’ve come across.